Question

S=\(1\times3+3\times5+5\times7+...+99\times101\)

Answer 1

S = 1.3 + 3.5 + 5.7 + ...+ 99.101

=>6S = 1.3.6 + 3.5.6 + 5.7.6 + ...+ 99.101.6

6S = 1.3.(5+1) + 3.5.(7-1) + 5.7.(9-3) + ...+ 99.101.(103-97)

6S = 1.3.5 + 1.3 + 3.5.7 - 1.3.5 + 5.7.9 - 3.5.7 + ...+ 99.101.103 - 97.99.101

6S = 1.3 + 99.101.103

S = 171 650

Answer 2

S = 1.3 + 3.5 + 5.7 + ...+ 99.101

=>6S = 1.3.6 + 3.5.6 + 5.7.6 + ...+ 99.101.6

6S = 1.3.(5+1) + 3.5.(7-1) + 5.7.(9-3) + ...+ 99.101.(103-97)

6S = 1.3.5 + 1.3 + 3.5.7 - 1.3.5 + 5.7.9 - 3.5.7 + ...+ 99.101.103 - 97.99.101

6S = 1.3 + 99.101.103

S = 171 650